SCALCET$94\mathrm{.}3\mathrm{.}009.$EP$.$

Consider the following function.

$f(x)=2x^3-18x^{2}48x-9$

Find the derivative.

$f^{\text{'}}(x)=$

$$

Find any critical numbers of the function. $($Enter your answer as a comma$-$separated list. If any answer does not exist, enter DNE$)$

$x=$

Find the interval$($s$)$ on which $f$ is increasing. $($Enter your answer using interval notation.$)$

$$

Find the interval$($s$)$ on which $f$ is decreasing. $($Enter your answer using interval notation.$)$

$$

Find the local minimum and maximum value of $f.$

local minimum value $$

local maximum value $$